Ideally, I'm looking for a github client for ipad (or whatever, at this point I'd be willing to buy an Android tablet just for that) that is designed for reading code that is on GitHub.
Yes, I have Working Copy. I also have several other applications that are in various ways related to git and github, but do not solve the problem.
> spend time manually cloning/syncing/resyncing/downloading/uploading repos. This quickly gets tedious
These should all take little-or-no-time and be far from tedious in any half-decent Git client. Have you tried Working Copy? (I haven't but it seems competent from reviews)